Interpreting DSGE Mathematics

To describe the mathematics of Dynamic Stochastic General Equilibrium (DSGE) as confusing is an understatement. Although trained in applied mathematics, I always had difficulties following the logic used. I now realise that the economists were not solving the global optimisation problem set out at the beginning of the paper. In fact, they are solving a different mathematical model. Importantly, this new formulation no longer solves the original optimisation problem. As a result, it is incorrect to assume that model behaviour reflects optimisation by households.

Fun With Central Bank Calvinball

In the comments to "Does the Governmental Budget Constraint Exist?" Nick Edmonds reminded about another piece of mainstream macro logic that triggers me: the governmental budget constraint holds, because the inflation-targeting central bank says so. From the perspective of a mathematician, this is just a variation of "because I want to assume it to be true." In this article, I run through whatever logic appears to exist.

Does The Governmental Budget Constraint Exist?

This article wraps up my discussion of the transversality condition and the governmental budget constraint. In summary, the governmental budget constraint used within mainstream macro has very serious flaws. I would have liked to use the title "The Governmental Budget Constraint Does Not Exist," but we need to take into account the rather curious Fiscal Theory of the Price Level. Furthermore, there are unsettling implications for the entire Dynamic Stochastic General Equilibrium (DSGE) model approach that relies upon optimisation. I abandoned looking at these models for this reason, and this article suggests why I believe the problems run much deeper. Unlike the previous articles, this article is largely free of mathematics, but I start out listing the various equations I refer to.

Mathematics Of The Budget Constraint (Again)

This article attempts to give a simpler mathematical discussion of the governmental budget constraint and transversality. After throwing my hands up in the air in my previous article, I run through the basic mathematics of the accounting identity for governments, and we can see that what is called "transversality" is just equivalent to making the assumption that the discounted primary surpluses converge to be equal to the initial stock of debt. However, household sector optimisation is nowhere in sight, which raises the question why it comes up in discussion of this topic in the first place.

Once again, the math-phobic may as well stay clear. I would also draw your attention to this article by Alex Douglas; he is jumping ahead to an extremely point about optimisations (in general, we have no reason to believe that the optimum exists when the set of solutions is not closed and finite).

On Being Pelted By Peanuts: Part I

Alexander Douglas (a lecturer in philosophy) wrote an interesting article on two subjects recently: "Macroeconomics -- A view from the peanut gallery." He covers two diverging topics: the transversality condition from mainstream macro, and the question of welfare functions in Stock-Flow Consistent models. I will take a stab at these topics over the coming days. In this article, I am expressing my deep displeasure with what is supposed to be trivial mathematics used by the mainstream: the transversality condition.

(He embeds some mathematics in his post, and so I am using MathJax to format an answer. The equations may not be properly rendered on some browsers. People who are allergic to equations may want to skip this one... I did this quickly, and already squashed a few typos.)

SFC Models And Introductory MMT-Style Fiscal Analysis

The usefulness of Stock-Flow Consistent (SFC) models is that they allow us to illustrate concepts in economics without relying solely on verbal descriptions. In this article, I will discuss my interpretation of some of the ideas floating around in Modern Monetary Theory (MMT). I will note that these are my interpretations of statements made by others, illustrated by an extremely simple model. The key is that even simple models can be used to clarify our thinking.

Weaknesses Of Term Premium Estimates Derived From Yield Curve Models

Term structure models have been a growth industry for researchers in academia and at central banks. These models can be structured in many different ways, which makes generalisations about them difficult. For the purposes of this article, I am only concerned about the use of these models to estimate a term premium that is embedded in nominal yields (although my comments can be extended to cover related exercises, such as calculating an inflation risk premium). When I examine individual models, the term premium estimates appear unsatisfactory, but the issues are different for each model. I believe that the root problems for this exercise are fundamental, and we need to understand these fundamental problems before looking at individual models.

Book Review: The Road To Ruin

James Rickards recently published The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis. His argument is that the risks of a financial crisis is building (possibly hitting in 2018), and that the financial system will be locked down as a result. (He argues that you need to buy gold to hedge against this.) The book is awkward, but has some interesting features. He describes various pop mathematics techniques for economic and financial analysis, although the book does not provide enough details to be able to evaluate them. James Rickards joined the LTCM hedge fund in 1994, and provides an insider's take on its collapse. He is also nostalgic for the economic framework of the 1950s, which parallels the views of a lot of post-Keynesians; the issue is that he is fixated on the gold peg, which was arguably an incidental feature of the 1950s economic institutions.

Low Bond Volatility Not Surprising

The low levels of implied volatility in the bond market has attracted a fair amount of commentary. Although it seems reasonable to believe that volatility selling strategies have reduced market volatility, there's no fundamental reason to expect a big reversal (outside of another crisis).

How To Approach The Term Premium

The term premium is an important concept in fixed income analysis. For our own analysis, there are a few ways of using the term premium. Unfortunately, there is no way of extending the analysis for an individual to the market in general, as there is no need for market participants to agree on the term premium before undertaking a transaction. As a result, we should not expect to be able to infer an average term premium implied by market pricing using any algorithm.

Primer: Fixed Income Arbitrage

The concept of arbitrage is important in financial theory, particularly in the bond market. For example, term premium estimates are derived from arbitrage-free term structure models. The simplest definition of arbitrage is the ability to lock-in risk-free profits (above the cost of capital); the usual efficient markets story is that arbitrageurs will trade in such a way to squash out such profits. This article explains how the term arbitrage is used in fixed income markets, and how this relates to ideas like arbitrage-free yield curve models. The discussion here avoids the use of mathematics, on the theory that anyone who understands financial market mathematics has already been introduced to the technical definition of arbitrage.

The Term Premium Problem

Discussions of the behaviour of term premia have come up recently in online discussion. (For example, among people I follow on Twitter.) When we discuss the term premium, we are usually discussing the estimates derived from arbitrage-free term structure models (such as affine term structure models). I am not a fan of these term premium estimates, but explaining my views has always been difficult. I have come to the conclusion that the mathematics behind these models is part of the problem, not part of the solution.

Bring On The Quantitative Tightening Debate

The debate around the Federal Reserve's balance sheet is starting to pick up. The Fed wants to reduce the size of its balance sheet (which will drain excess reserves from the system), which reverses Quantitative Easing (QE). For simplicity, I will call this policy Quantitative Tightening (QT). If the policy is implemented on the basis that it is a substitute for rate hikes for a period of time, bond yields should be expected to fall. This will cause predictable consternation among some commentators.

A SFC Model Of Gold Standard Austerity Policies

This article describes the model that I discussed in an earlier video (video link: https://youtu.be/Sx6YkT75ehg). Although a Gold Standard is not exactly a pressing topic for most of us, the simplicity of the system makes it easy to demonstrate ways in which we can use stock-flow consistent (SFC) models. In this case, I can explain why austerity was a core component of gold standard thinking.

Video: sfc_models Equation Solver

Video running through some of the technical issues in the equation solver that is embedded in the Python sfc_models framework. The solver used is the standard iterative search used in fixed point theorems, with a small tweak that allows convergence even when the equations are poorly conditioned for the algorithm. In the example, the equation that determines how the central bank cancels gold flows in my gold standard model is the source of ill conditioning.

Book Review: The Benefit And The Burden

Bruce Bartlett published "The Benefit and the Burden: Tax Reform -- Why We Need It And What It Will Take" in 2012. The book offers an introduction to how tax policy is set in the United States. The political situation has obviously changed since the book was published, but the historical background is useful to provide context. The text is definitely not "in paradigm" with Modern Monetary Theory (MMT), but this does not matter when discussing the narrow topic of tax reform. This article also explains why I am skeptical that tax reform will be passed any time soon.